Is there any reference which claims that all of them need to have the same structure? Lanthanides have a quite complicated shell structure, so if someone told me that there was polymorphism and different crystallization conditions lead to different structures I would believe that immediately.

Jürgen Weippert

There are many references and few of them included below:

For dodecahedral structure:

[1] J. Saha, Y.M. Jana, G.D. Mukherjee, R. Mondal, S. Kumar, H.C. Gupta,

Structure, Mössbauer spectroscopy and vibration phonon spectra in valence-bond force-field model approach for distorted perovskites AFeO3 (A = La, Y), Materials Chemistry and Physics (2019), doi: https://doi.org/10.1016/j.matchemphys.2019.122286.

[2] Seung-Joo Kim et al., Journal of Solid State Chemistry 161, 197-204 (2001).

[3] R. DOGRA et al., Hyperfine interaction measurements in LaCrO3 and LaFeO3 perovskites using perturbed angular correlation spectroscopy, PHYSICAL REVIEW, B 63 224104.

[4] R.T.A. Khan et al., Crystal structure of LaVO3 by Rietveld refinement method, Materials Letters 58 (2004) 1737–1740

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For cuboctahedral structure:

[1] Graham King and Patrick M. Woodward, Cation ordering in perovskites, J. Mater. Chem., 2010, 20, 5785–5796

[2] E. 632 Haye et al., Properties of rare-earth orthoferrites perovskite driven by steric hindrance, Journal of Alloys and Compounds 657 (2016) 631-638.

[3] R.T.A. Khan et al, Crystal structure of LaVO3 by Rietveld refinement method, Materials Letters 58 (2004) 1737–1740.

[4] I. R. Shein et al., Band Structure and the Magnetic and Elastic Properties

of SrFeO3 and LaFeO3 Perovskites, Physics of the Solid State, Vol. 47, No. 11, 2005, pp. 2082–2088. Translated from Fizika Tverdogo Tela, Vol. 47, No. 11, 2005, pp. 1998–2003.

[5] I. R. Shein, K. I. Shein, V. L. Kozhevnikov, and A. L. Ivanovskiœ, Band Structure and the Magnetic and Elastic Properties of SrFeO3 and LaFeO3 Perovskites, Physics of the Solid State, 47 (2005) 2082–2088.

In LaFeO3, each La3+ ion is coordinated by twelve oxygen ions, forming a polyhedral structure around the La3+ ion. This polyhedral structure is close to a cuboctahedron, which is a polyhedron with eight triangular faces and six square faces. However, the actual shape of the oxygen polyhedron around La3+ is distorted due to various factors, such as the size of the ions and the chemical bonding interactions. Experimental studies and theoretical calculations have shown that the oxygen polyhedron surrounding La3+ in LaFeO3 is best described as a distorted cuboctahedron, where the square faces are slightly compressed and the triangular faces are slightly elongated. This distortion is a result of the Jahn-Teller effect, which arises due to the degeneracy of the d-orbitals of the Fe3+ ions in the crystal structure.